Answer:
b. reflection
Step-by-step explanation:
just took the test
Answer:
x=13 /6
Step-by-step explanation:
Answer:6over2
Step-by-step explanation:
Answer:
The correct option is d
Step-by-step explanation:
From the question we are told that
The population size is ![N = 47000](https://tex.z-dn.net/?f=N%20%20%3D%20%2047000)
The sample size is ![n = 200](https://tex.z-dn.net/?f=n%20%20%3D%20%20200)
The sample mean is ![\= x = 118.0 \ mmHg](https://tex.z-dn.net/?f=%5C%3D%20x%20%20%3D%20%20118.0%20%5C%20mmHg)
The standard deviation is ![\sigma = 11.0 \ mmHg](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%2011.0%20%5C%20mmHg)
Given that the confidence level is 95% then the level of significance can be calculated as
![\alpha = 100 - 95](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%20100%20-%20%2095)
![\alpha = 5 \%](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%205%20%5C%25)
![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%200.05)
Next we obtain the critical value of
from z-table , the value is ![Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 1.96](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%20%7D%20%3D%20%20Z_%7B%5Cfrac%7B0.05%20%7D%7B2%7D%20%20%7D%20%3D%201.96)
The reason we are obtaining critical value of
instead of
is because
represents the area under the normal curve where the confidence level interval (
) did not cover which include both the left and right tail while
is just the area of one tail which what we required to calculate the margin of error
.
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
Generally the margin of error is mathematically represented as
![E = Z_{\frac{\alpha }{2} } *\frac{\sigma }{ \sqrt{n} }](https://tex.z-dn.net/?f=E%20%20%3D%20%20Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%2A%5Cfrac%7B%5Csigma%20%7D%7B%20%5Csqrt%7Bn%7D%20%7D)
substituting values
![E = 1.96 *\frac{11.0 }{ \sqrt{200} }](https://tex.z-dn.net/?f=E%20%20%3D%20%201.96%20%2A%5Cfrac%7B11.0%20%20%7D%7B%20%5Csqrt%7B200%7D%20%7D)
![E = 1.5245](https://tex.z-dn.net/?f=E%20%20%3D%201.5245)
The 95% confidence level interval is mathematically represented as
![\= x - E < \mu < \= x + E](https://tex.z-dn.net/?f=%5C%3D%20x%20%20-%20%20E%20%3C%20%5Cmu%20%3C%20%5C%3D%20x%20%20%2B%20%20E)
substituting values
![118.0 - 1.5245 < \mu < 118.0 + 1.5245](https://tex.z-dn.net/?f=118.0%20%20%20-%20%201.5245%20%3C%20%5Cmu%20%3C%20118.0%20%20%20%2B%20%201.5245)
![116.5< \mu < 119.5](https://tex.z-dn.net/?f=116.5%3C%20%5Cmu%20%3C%20119.5)
![[116.5 , 119.5]](https://tex.z-dn.net/?f=%5B116.5%20%2C%20119.5%5D)